A teenager can legally own a long gun so I would talk to my parents and explain to them that you don’t feel safe without a defensive weapon in the house. The break-in is proof that it can occur in your own home. Find a local firearms training course and get the whole family to take part.
Minimum Age for Gun Possession: Federal law prohibits, with certain exceptions*, the possession of a handgun or handgun ammunition by any person under the age of 18. Federal law provides no minimum age for the possession of long guns or long gun ammunition.
Several states and the District of Columbia impose minimum age requirements that extend beyond those contained in federal law.
Oddly this info come from an anti firearms ownership site: http://smartgunlaws.org/minimum-age-to-purchase-possess-firearms-policy-summary/ There is a table with age restrictions for each state on the page.